NDLI: On multifractal of Cantor dust

Content Provider	Springer Nature Link
Author	Baek, In Soo
Copyright Year	2009
Abstract	We consider quasi-self-similar measures with respect to all real numbers on a Cantor dust. We define a local index function on the real numbers for each quasi-self-similar measure at each point in a Cantor dust. The value of the local index function at the real number zero for all the quasi-self-similar measures at each point is the weak local dimension of the point. We also define transformed measures of a quasi-self-similar measure which are closely related to the local index function. We compute the local dimensions of transformed measures of a quasi-self-similar measure to find the multifractal spectrum of the quasi-self-similar measure. Furthermore we give an essential example for the theorem of local dimension of transformed measure. In fact, our result is an ultimate generalization of that of a self-similar measure on a self-similar Cantor set. Furthermore the results also explain the recent results about weak local dimensions on a Cantor dust.
Ending Page	1182
Page Count	8
Starting Page	1175
File Format	PDF
ISSN	14398516
e-ISSN	14397617
Journal	Acta Mathematica Sinica, English Series
Issue Number	7
Volume Number	25
Language	English
Publisher	Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Publisher Date	2009-06-15
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cantor set Hausdorff dimension quasi-self-similar measure local dimension Fractals Mathematics packing dimension Hausdorff and packing measures
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Density theorems for Hausdorff and packing measures of self-similar sets

Self-similar structure on intersection of Cartesian product of Cantor triadic sets with their translations

Hausdorff Measure of Homogeneous Cantor Set

Random self-affine multifractal Sierpinski sponges in $${\mathbb{R}^d}$$

A Cantor set in the plane and its monotone subsets

Dimensions of random self-affine multifractal Sierpinski sponges in $${{\mathbb{R}}^d}$$

Multifractal formalism for self-affine measures with overlaps

Multifractality of overlapping non-uniform self-similar measures

The Hausdorff dimension of sets related to the general Sierpinski carpets

On multifractal of Cantor dust

Similar Documents

Density theorems for Hausdorff and packing measures of self-similar sets

Self-similar structure on intersection of Cartesian product of Cantor triadic sets with their translations

Hausdorff Measure of Homogeneous Cantor Set

Random self-affine multifractal Sierpinski sponges in $${\mathbb{R}^d}$$

A Cantor set in the plane and its monotone subsets

Dimensions of random self-affine multifractal Sierpinski sponges in $${{\mathbb{R}}^d}$$

Multifractal formalism for self-affine measures with overlaps

Multifractality of overlapping non-uniform self-similar measures

The Hausdorff dimension of sets related to the general Sierpinski carpets

On multifractal of Cantor dust